Problem: $-1\dfrac{1}{6} \div 2\dfrac{1}{3} = $
Explanation: Let's start by converting the mixed numbers to fractions. $\phantom{=}-1\dfrac{1}{6} \div 2\dfrac{1}{3}$ $=-\dfrac{7}{6}\div\dfrac{7}{3}$ $=-\dfrac{7}{6}\cdot\dfrac{3}{7} ~~~~~~~\text{multiply by the reciprocal}$ $=-\dfrac{{1}\cancel{7}}{6}\cdot \left(\dfrac{3}{{1}\cancel{7}}\right)$ $=-\dfrac{1}{{2}\cancel{6}}\cdot\left(\dfrac{{1}\cancel{3}}{1}\right)$ $=-\dfrac{1}{{2}}\cdot\left(\dfrac{{1}}{1}\right)$ $=-\dfrac{1}{2}$